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Markovian approximation to the finite loci coalescent with recombination along multiple sequences

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  • Hobolth, Asger
  • Jensen, Jens Ledet

Abstract

The coalescent with recombination process has initially been formulated backwards in time, but simulation algorithms and inference procedures often apply along sequences. Therefore it is of major interest to approximate the coalescent with recombination process by a Markov chain along sequences. We consider the finite loci case and two or more sequences. We formulate a natural Markovian approximation for the tree building process along the sequences, and derive simple and analytically tractable formulae for the distribution of the tree at the next locus conditioned on the tree at the present locus. We compare our Markov approximation to other sequential Markov chains and discuss various applications.

Suggested Citation

  • Hobolth, Asger & Jensen, Jens Ledet, 2014. "Markovian approximation to the finite loci coalescent with recombination along multiple sequences," Theoretical Population Biology, Elsevier, vol. 98(C), pages 48-58.
    • Handle: RePEc:eee:thpobi:v:98:y:2014:i:c:p:48-58
    DOI: 10.1016/j.tpb.2014.01.002
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    References listed on IDEAS

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    1. Heng Li & Richard Durbin, 2011. "Inference of human population history from individual whole-genome sequences," Nature, Nature, vol. 475(7357), pages 493-496, July.
    2. Thomas Mailund & Julien Y Dutheil & Asger Hobolth & Gerton Lunter & Mikkel H Schierup, 2011. "Estimating Divergence Time and Ancestral Effective Population Size of Bornean and Sumatran Orangutan Subspecies Using a Coalescent Hidden Markov Model," PLOS Genetics, Public Library of Science, vol. 7(3), pages 1-15, March.
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    Cited by:

    1. Miroshnikov, Alexey & Steinrücken, Matthias, 2017. "Computing the joint distribution of the total tree length across loci in populations with variable size," Theoretical Population Biology, Elsevier, vol. 118(C), pages 1-19.
    2. Carmi, Shai & Wilton, Peter R. & Wakeley, John & Pe’er, Itsik, 2014. "A renewal theory approach to IBD sharing," Theoretical Population Biology, Elsevier, vol. 97(C), pages 35-48.
    3. Deng, Yun & Song, Yun S. & Nielsen, Rasmus, 2021. "The distribution of waiting distances in ancestral recombination graphs," Theoretical Population Biology, Elsevier, vol. 141(C), pages 34-43.
    4. Hobolth, Asger & Siri-Jégousse, Arno & Bladt, Mogens, 2019. "Phase-type distributions in population genetics," Theoretical Population Biology, Elsevier, vol. 127(C), pages 16-32.

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